Question: All of the 4th grade teachers and students from Santa Rita went on a field trip to an art museum. Tickets were $$5.50$ each for teachers and $$4.00$ each for students, and the group paid $$56.50$ in total. A few weeks later, the same group visited a natural history museum where the tickets cost $$11.00$ each for teachers and $$10.50$ each for students, and the group paid $$138.00$ in total. Find the number of teachers and students on the field trips.
Explanation: Let $x$ equal the number of teachers and $y$ equal the number of students. The system of equations is: ${5.5x+4y = 56.5}$ ${11x+10.5y = 138}$ Solve for $x$ and $y$ using elimination. Multiply the top equation by $-2$ ${-11x-8y = -113}$ ${11x+10.5y = 138}$ Add the top and bottom equations together. $ 2.5y = 25 $ $ y = \dfrac{25}{2.5}$ ${y = 10}$ Now that you know ${y = 10}$ , plug it back into $ {5.5x+4y = 56.5}$ to find $x$ ${5.5x + 4}{(10)}{= 56.5}$ $5.5x+40 = 56.5$ $5.5x = 16.5$ $x = \dfrac{16.5}{5.5}$ ${x = 3}$ You can also plug ${y = 10}$ into $ {11x+10.5y = 138}$ and get the same answer for $x$ ${11x + 10.5}{(10)}{= 138}$ ${x = 3}$ There were $3$ teachers and $10$ students on the field trips.